1. Field of the Invention
The present invention relates to a servo control method using a reference trajectory, and more particularly, to a servo control method of controlling a plant to track a reference trajectory with enhanced accuracy using a reference signal and its derivative signals, and an apparatus and a recording medium suitable for the same.
2. Description of the Related Art
In general, a hard disk drive (HDD), which is a data storage device in a computer system for reproducing and writing data on a disk.
The HDD includes a head disk assembly (HDA) and a printed circuit board (PCB) assembly for writing and reading information by electrically controlling the HDA, wherein the HDA includes heads for storing or reproducing information, disks on which the information is recorded by the heads, a spindle motor for rotating the disks, an actuator arm for moving the heads, a voice coil motor (VCM), and an outer disk crash stop (ODCS) and an inner disk crash stop (IDCS) for limiting displacement of the actuator arm.
The ODCS and IDCS are stoppers for limiting the displacement of the actuator arm to prevent the heads from moving to locations at which servo information of the discs are not written.
A general tendency of the HDD industry is to decrease the physical size of storage devices while at the same time increasing information capacity. This is achieved by an increase of track density of HDDs. Servo tracks are sources for location information during an operation of an HDD. As a result, there are two main trends in servo writing of the HDD. One is to increase the accuracy for servo track writing, and the other is to develop new ways for servo track writing. U.S. Pat. No. 5,668,679 discloses a spiral self servo writing method of writing a plurality of reference servo signals on a disk in a spiral shape and writing a final servo signal based on the reference servo signals. Since accuracy of the reference servo signals determines the quality of the final servo signal, it is important to manage strictly the accuracy of the reference servo signals. That is, the positioner for controlling movement of the write heads for writing the reference servo signals must be accurate.
Due to an industrial tendency for higher accuracy, it is now important to consider several physical phenomena in controlling servo writing. Examples of such phenomena are friction, mechanical delay and torsion effect. A problem attendant with controlling such phenomena is that the forces describing these phenomena are very non-linear. Moreoever, even if it is possible to model these phenomena, such modeling is very complicated and requires significant experimentation and specialized knowledge. In addition, new methods for self servo writing also present new problems.
FIG. 1 is a block diagram of a conventional PID controller 102. PID controlling, which is the most frequently used method among automatic control methods, is performed using a combination of proportion, integral and differential operations.
Referring to FIG. 1, r(t) denotes a reference signal, y(t) denotes a position measurement signal, e(t) denotes an error signal provided to the PID controller 102, and u(t) denotes a control signal.
A conventional servo writing operation provides a constant reference signal having a relatively long period. According to this control algorithm, it is known that this situation establishes a point reference tracking. As a result, derivatives of the constant reference signal are 0 (zero) during a servo writing operation.
According to the development of new servo writing methods, location information is encoded on the disk in another pattern, and the reference location varies according to a location encoding method during servo writing.
This results in non-zero derivatives of the reference signal. A feedback controller is designed to ensure that the position of the servo track writing head follows a desired reference trajectory with exact and very high accuracy. Control by the PID controller 102 can be considered feed forward control. Using the feed forward control, complicated trajectories can be tracked with high accuracy.
Another important contribution of the derivative feed forward control is tracking at higher speed as shown in FIG. 2.
FIG. 2 is a diagram illustrating an effect of the feed forward control.
As shown in FIG. 2, a pure PID control needs a time Ta in order to adapt to a ramp reference signal. The ramp reference signal has a constant slope. A position PID control and a feed forward control can theoretically provide fast tracking with respect to the ramp reference signal for an integrator plant, where the term “integrator plant” should be easy to understand for one of ordinary skill in the art. The integrator plant has a transfer function containing the term 1/s.
However, a problem is that a mechanical system used for servo track writing has nonlinear characteristics. As described above, the nonlinear characteristics include friction, mechanical delay and a torsion effect. As a result of higher accuracy requirements, the relative importance of these nonlinear characteristics has increased. FIGS. 3(a) and 3(b) show the influence of friction on a typical movement.
FIGS. 3(a) and 3(b) show diagrams illustrating the influence from friction in a plant. FIG. 3(a) shows a comparison of a reference trajectory of a plant (e.g., a write head of a servo writer) to an actual trajectory, and FIG. 3(b) shows a comparison of a reference value of a current supplied to a plant (e.g., a VCM for moving the write head) to obtain the movement shown in FIG. 3(a).
Referring to FIGS. 3(a)-3(b), the plant vibrates with a limited cycle while tracking the reference trajectory. The vibration of the plant is nonlinear whereas the control system is linear. This vibration may be prevented by fine tuning in certain cases. However, determining appropriate values is difficult. Furthermore, success is not always guaranteed. This limited cycle, for example, may provide an undesirable effect to forming of a servo track pattern.
Other approaches to guarantee the higher accuracy requirements are necessary. These approaches may include nonlinear controllers. A design of a high performance controller based on physical principles is time-consuming requiring very difficult and high-leveled specialized knowledge and significant experimentation. It is preferable to avoid those complicated approaches by using neural networks performing nonlinear control for controlling plants.
In computer science and engineering, artificial neural networks are inspired by structures of biological neurons. It is known that the neural networks can learn a pattern of nonlinear operations in a wide range. Characteristics of the neural networks are frequently used to control operations of a highly nonlinear and complicated system. Different neural network structures are used for different subjects.
FIG. 4 is a block diagram of a controller having a conventional PID controller and a conventional feed forward neural network. The controller shown in FIG. 4 includes a PID controller 402 and a feed forward neural network 404.
However, the controller does not use derivative information of a reference signal. Besides, a closed-loop control is still linear, and therefore there is no guarantee that the limited cycle and other nonlinear effects illustrated in FIGS. 3(a) and 3(b) will be removed.
FIG. 5 shows a feedback neural network.
FIG. 5 is a block diagram of a controller having a conventional feedback neural network. The controller shown in FIG. 5 includes a feedback neural network 504.
The feedback neural network 504 may learn by using a plurality of different methods (e.g., a direct inverse control, an optimal control, an internal model control, etc., as is known by those skilled in the art). Only an appropriately controlled neural network avoids the limited cycle.
One problem of this approach is that it is difficult to avoid a zero steady state error even for constant velocity reference signals. This is because it is difficult to obtain an integral of the controller that can guarantee the zero steady state error. An exemplary system of a non-zero steady state error is shown in FIG. 6.
FIG. 6 is a diagram illustrating an offset error (non-zero steady state error) of a closed-loop system.
The non-zero steady state error shown in FIG. 6 is also not preferable during the servo track writing.
Another related technical problem is that online generation of a reference trajectory should be tracked. A present approach is to define a desired standard location by assuming that samplings of a digital control system are constant at each sampling. Though this is an effective approach, accuracy requirements increasing with respect to the servo track writing require a decrease of the sampling period, thereby making use of a lookup table inconvenient from a size standpoint.